- I

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1. AGWIV UN ONLY (LUS B 1 IEPORT DATA '. 'o, TTMA AIM DATES WWWS__ January 26. 1993 tAnnual Technical 11/92 - 12/31192

. UAND SUUnI I. FuuMs INNAU

(U) Development of Predictive Reaction ModelAof Soot PFE - 61102F

FormtionPR - 2308SA -BS

L AUTrOWA G - AFOSR 91-0129

7. PEFOG OSGANIZATMON NAW|S) AND is t L P140)

Pennsylvania State UniversityyUniversity Park, PA 16802

AFOSR-T `3 `7

9. SPOOSOIG/IN1ITQJNG AGINCY NAMEIS) AND AOORISS4ES) 93-04297AFOSR/NA110 Duncan Avenue, Suite B115 Il 11 MI IIIil II1 1111 llIII' 0Bo1•i, A•B DX 20332-0001"• if

11. SUPPLEMENTART NOTES

12a. DS•fhUTI•JAVAULAM' STATEMNT 12L. OISTANUTION COME

Approved for public release; distribution isunlimited

13. A'STRACT (Mnaum JOQ woo ...During the second twelve-month period of the project, progress has been made inthe following areas: (1) The computational study of sooting limits in laminarpremixed flames was completed. It was found that the critical equivalence ratiosfor soot appearance, both the absolute values and temperature dependencieS, can bepredicted fairly close to the experimental observations. Sensitivity and reaction-path analyses were performed co examine the factors responsible for the predictedbehavior. (2) New estimation Lechniques were developed and applied for calcula-tions of standard-state enthaLpies of formation and binary gaseous diffusion coef-ficients of polycyclic aromatic hydrocarbons (PARs) and their radicals, thus pro-

C1"1 viding critical information -f)r accurate modeling of soot formation in flames.(3) Theoretical studies of a bench-mark ion-molecule reaction were completed. (4)

C Computer simulations of the effect of pressure on soot formation were initiated.(5) Several manuscripts summarizing the results obtained have been completed andsubmitted for publication.

I'4 SUBJECT TERMS I1L NUMBER Of PAGES18

Soot Formation, Computer Modeling i. PIE CODE

17 SECURITY CIASSFICATION 1e. SECURITY CLASSIFICATION It. SECURETr (.ASS11CATIOC O 2L UMITATION OF AISTRACTOF REPORT OP THIS PAGE OF ASSTRACTUnclassif ied Unclassified Unclassified UL

NSN 7S40-01I.Jso.sm stati.ri Pfcm .. 8 t5104 oraft.

DEVELOPMENT OF PREDICTIVE REACTION MODELS

OF SOOT FORMATION

Annual Technical Report

Grant No. AFOSR 91-0129

Covering the period from January 1, 1992 to December 31. 1992

prepared for

AIR FORCE OFFICE OF SCIENTIFIC RESEARCH

Boiling AFB

Accesion For

NTIS CRA&M

b y DTIC TABUnannounced E_

Michael Frenklach and Hai Wang Justification .........................

Fuel Science Program Distribution I

Department of Materials Science and Engineering Availability CodesThe Pennsylvania State University -

University Park, PA 16802 Avail and/orSpecial

January 26, 1993

TABLE OF CONTENTS

INTRODUCTION................................. 4

WORK PROPOSED ....................... ....... 4

ACCOMPLISHMENTS ............................. 4

RESU LTS ...................................... 5

Sooting Limits in Laminar Premixed Flames ........... 5

Evaluation of the Enthalpies of Formation ofPAH Molecules and Radicals ............... 8

Transport Properties of Polycyclic AromaticHydrocarbons ........................ 11

Semiempirical Quantum-Mechanical and RRKM Studiesof Reaction C8H7' + C2H2 -- C10H9 . . . . . . . 15

FUTURE W ORK ................................ 16

PRESENTATIONS AND PUBLICATIONS .............. 16

PROFESSIONAL PERSONNEL ..................... 17

INVENTIONS .................................. 17

REFERENCES ................................. 18

3

INTRODUCTION

This is a second-year annual report on the project. The ultimate objective of this program is todevelop a predictive reaction model for soot formation in hydrocarbon flames. The specificobjectives of the proposed 3-year study are: 1) To extend the modeling efforts to computersimulation and analysis of more complex sooting phenomena, such as sooting limits in laminarpremixed flames, soot formation in premixed flames of aromatic fuels, and soot formation inlaminar diffusion flames, and 2) Further refinement of the underlying reaction mechanism of sootformation.

WORK PROPOSED

The specific objectives for the past year were:

I. To complete simulations of the sooting limits in a series of laminar premixed flames andexamine the results.

2. To complete the revision and testing of the neutral reaction mechanism of PAH formation andgrowth.

3. To revise the computer code for soot particle nucleation and growth, i.e., to insert the opticalmodel developed into our main soot-kinetics code.

4. To perform quantum-chemical calculations on additional ion-molecule reactions of interest tothe ionic mechanism of soot formation and perform the associated rate-coefficient calculations.

5. To initiate a computational study of pressure effect on soot formation since this subject is ofinterest due to growing concern over controlling soot emission from practical combustiondevices.

6. To prepare manuscripts reporting the results of (1) - (4) above.

ACCOMPLISHMENTS

During the second twelve-months period of the project, progress has been made in all theareas, (1)-(5) above. The principal accomplishments of the past year are the following: (I) Thecomputational study of sooting limits in laminar premixed flames was completed. It was foundthat the critical equivalence ratios for soot appearance, both the absolute values and temperaturedependencies, can be predicted fairly close to the experimental observations. Sensitivity andreaction-path analyses were performed to examine the factors responsible for the computedbehavior. (2) New estimation techniques were developed and applied for calculations of standard-state enthalpies of formation and binary gaseous diffusion coefficients of polycyclic aromatichydrocarbons (PAHs) and their radicals, thus providing critical information for accurate modelingof soot formation in flames. (3) Theoretical studies of a bench-mark nn-molecule reaction werecompleted. (4) Computer simulations of the effect of pressure on soot formation were initiated.(5) Several manuscripts summarizing the results obtained have been completed and submitted forpublication. The results obtained are detailed below.

4

RESULTS

Sooting Limits in Laminar Premixed Flames

The critical equivalence ratios were determined for several atmospheric laminar premixedflames of C2-fuels: ethane, ethylene and acetylene. The value of the critical equivalence ratio, O,for a given fuel and a given maximum flame temperature, Tm, was determined by computingflames with different equivalence ratios. The maximum flame temperature in these runs wasmaintained approximately the same by adjusting, similarly to the experiment, the amount of N2 inthe mixture. For each of the fuels, at least two series of flames were simulated, each at a differentmaximum flame temperature, in order to test the temperature dependence predicted for Oc.

The numerical simulation of soot particle formation was performed in two stages: first, theproduction of the initial PAH species; and second, PAH further growth and nucleation and growthof soot particles. In the first stage, PAH formation up to coronene was simulated in a burner-stabilized flame configuration with a specified temperature profile and flow rate. The temperatureprofile and the flow rate were those computed from an equivalent free adiabatic flame, with onlysmall-hydrocarbon chemistry included (primarily C1 to C4 , 32 species, 139 reactions). In otherwords, the free-flane simulation with the reduced chemistry was used to determine the initialconditions, temperature profile and gas velocity for the subsequent burner-stabilized flamesimulation with the "full" chemistry that included the desired PAH formation and growth reactions.Such two-step "free flame" simulations were almost identical, with respect to the predictedconcentrations of the principal radicals and molecular products, to equivalent free flames computedwith the "full" reaction mechanism. Yet, splitting the calculations in this fashion saved substantialamounts of computational time.

The maximum temperature reached in the free-flame simulation, with a given 0, was matchedto the corresponding experimental value measured by Harris et al.I. The adjustment of themaximum flame temperature was accomplished, similarly to the experiment, by varying the amountof N2 present in the mixture, but not necessarily equal to the experimental level of dilution, andbeing typically 5 % higher in N2 mole fraction.

All the calculations in the first stage were carried out with the Sandia burner code, 2 usingforward differencing on the convective terms with a mesh consisting of 160-210 grid points. Theruns were performed without considering thermal diffusion. The effect of thermal diffusion is notsignificant at the conditions of interest to the present study, as was found out in test runs.

In the second stage, the profiles of H, H2 , C2H 2 , 02, OH, H,0 and acepyrene (A4 R5)obtained in the flame simulation were used as input for the simulation of the growth of PAHsbeyond acepyrene by the technique of chemical lumping and the soot particle nucleation andgrowth by a method of moments. The calculations were performed using an in-house kinetic code.The mathematical and computational details of this part of the model can be found in Ref. 3.

The gas phase and surface reaction mechanisms used in both stages of the calculations wereessentially the same as the ones developed earlier. 3.4 Briefly, the reaction mechanism used in thefirst stage consisted of 337 reactions and 70 chemical species and included a detailed description offuel pyrolysis and oxidation and the formation and growth of aromatics up to coronene. Thechemical model used in the second stage describes the growth of PAHs beyond acepyrene, the

5

coagulation of the planar PAHs into spherical particles and the growth of the resulting particles bycoagulation and surface growth via PAH condensation and heterogeneous reactions with C2H 2.The surface processes were described in terms of elementary chemical reactions of active surfacesites. The oxidation of the soot particles was described by the reactions of active surface sites with

02 and of soot particles with OH. The rates of the surface reactions were expressed aspreviously,

3

kg,s Cg a XS S

where kg,s is the per site rate coefficient, Cg the concentration of the colliding gaseous species g, athe fraction of surface sites available for a given reaction, .zs the number density of surface sites,and S the total particle surface area. The steric factor a was introduced4 to account for thefraction of surface carbon sites capable. of undergoing growth reactions with C2H2 and oxidationwith 02. In the present work, this steric property was represented as a function of the maximumflame temperature in the form

a = 2[tanh(1218 0- - 7.19) + 1]

Such representation warrants that a approaches unity at the low temperature limit, implying that inthis limit the outer carbon atoms of the soot particle comprise a locally open structure such thatevery carbon site is available for further reaction, and becomes zero at an infinitely hightemperature, when the annealing covers the particle with the unreactive basel planes of the aromaticrings. The above expression was obtained by fitting the values of a determined in the previousstudy,4 i.e., a = 0.1 at 2000 K and a = 0.7 at 1600 K.

In the experiments of Harris et al.,I the critical equivalence ratio for the appearance of sootwas determined by observing the onset of yellow light emission in a flame. To be consistent withthis, the critical equivalence ratio Oc in our simulations was determined from the computedluminous intensity flux emitted by soot particles. 3 We assumed that the critical equivalence ratio isreached when the luminous intensity flux undergoes a sudden rise, i.e., the critical 0 is defined atthe point of maximum curvature in the normalized luminous flux plotted against the equivalenceratio, or in practical terms, by the intercept on the O-axis made by the line tangential to this curve.Associated with some uncertainty, this procedure was found to provide a most consistent way ofobtaining Oc in the present modeling study, in light of the lack of quantitative information for theonset of soot appearance in the comparable experimental studies. Such determination procedurewas found to be also consistent with the spectral sensitivity of the human eye: assuming a circularburner with a diameter of 6 cm and an observer's eye located at a distance of 50 cm from the sootinception zone, the absolute value of the radiant flux calculated at the critical equivalence ratiodetermined in the manner described above is of the same order of magnitude with the absolutethreshold of human vision (the latter data are taken from Wald5 ).

The critical equivalence ratios determined in this manner for the three fuels are displayed inFig. 1, where they are compared with the experimental data of Harris et al. 1 As can be seen in thisfigure, the computed critical equivalence ratios follow the correct temperature dependence for eachfuel, i.e., the critical equivalence ratio increases as the flame temperature increases, and the correctdependence on fuel type, for a constant flame temperature Tm, i.e., acetylene soots earlier than

6

ethylene which soots earlier than ethane. The quantitative agreement between the computed andexperimental values of O is also reasonable, considering the lack of the precise experimental datafor model input and boundary conditions, uncertainties in the model parameters, and the fact thatthe reaction mechanism was adopted from the previous study4 without any adjustments.

The analysis of the computational results strongly suggested that the appearance of soot andhence the sooting limits in these flames is controlled by two factors: concentration of acetylene andthe growth of PAHs. The second factor-the PAH build-up--is limited by the rise in flametemperature towards the end of the main reaction zone. The oxidation of PAHs, the molecularprecursors to soot particles, was not found to be a controlling factor. This does not mean,however, that hydrocarbon oxidation does not play a role in soot formation. On the contrary,oxidation of pre-aromatic-ring species, like C2H 3 by 02, determines to a great degree theconcentration level of phenyl, the first aromatic ring. Also, the oxidation of PAHs by OH beginsto be more pronounced in locations away from the main flame zone, where OH becomes thedominant oxidant.

Tm (K)

1900 1800 1700 16002.2 i

2.0

--

0

S1.8 0

1 .6 0

0

1.45.2 5.6 6.0 6.4

1, / Tm (K-1)

Figure 1. Comparison of the computed and experimentally determined critical equivalence ratios 0for ethane, ethylene and acetylene flames, as a function of the maximum flametemperature Tm. The open symbols represent the experimental data of Harris et al.,1

solid lines-linear fits to the experimental points, and solid symbols-the presentcomputational predictions.

7

Evaluation of the Enthalpies of Formation of PAH Molecules and Radicals

As part of the ongoing efforts on soot formation model development and refinement, theenthalpies of formation of polycyclic aromatic hydiocarbon (PAH) molecules, radicals andsubstituted aromatics were investigated. The enthalpy data used in previous and current modelingefforts have been mainly derived from Benson's group additivity method. 6 Recent results from abinitio quantum mechanical calculations have shown that for large peri-condensed PAHs, theenthalpies of formation predicted by the group additivity method could be off by as much as 10kcal/mol. 7 The objective of the present work was to determine accurately the enthalpies of forma-tion for the major aromatic species involved in the growth of PAHs and soot in high-temperatureenvironments. These species include PAH molecules up to 3-circumcoronene, PAH radicals up tocoronyl, and some substituted aromatics.

A method for accurate and economical estimation of the enthalpies of formation for benzenoidaromatic species was developed which combines semiempirical quantum-mechanical calculationswith group c-irrections. In this method, the deviation between experimental and calculatedenthalpies of formation is partitioned into structural groups. The general idea is to use a calculationmethod which is computationally less demanding than quantum ab initio but physically morerealistic than group-additivity calculations, and then to correct the results using a group-additivityscheme for the numerical inaccuracy of the semiempirical quantum-chemical method. Theadvantage of this approach is that it can be applied consistently to both molecules and radicals. Theresults of the present study demonstrate that the suggested approach is capable of accurateestimation of Af-298 for benzenoid aromatics.

The AM1 method of the AMPAC and MOPAC computer packages was used for thecalculations. The AM1-group correction (AMI-GC) method developed here assumes that thedeviation between the experimental and calculated enthalpies of formation can be partitioned intostructural groups that comprise the chemical species. It is further assumed that the groupcorrection of a given structural group is independent of the overall molecular structure. If wedenote the contribution of the ith structural group to the overall deviation by a group correctionproperty, GCi, the enthalpy of formation (AfH 98) can be expressed by

N

AfH;98 = Af/H29 x (AM)) - Y GCi (1)i=1

where AfH' 98 (AM 1) is the AMI enthalpy of formation and N the total number of the structuralgroups. The group assignment was the same as that of Benson's group-additivity method, i.e.,one perimeter C-H group, [CB-(H)I, and three fused-carbon groups, [CF-(CB)2(CF)I,[CF--(CB)(CF)2] and [CF-(CF) 31.

The GC values for the aromatic groups described above were derived by weighted least-squares minimization of

K N 12

X wk AfH98,k(expt)-Af!I 98,k(AMl) + Z GCi (2)k= Ii

where AfHI 98.k(expt) is the experimental enthalpy of formation of the kth compound, wk theweight factor, Nk the total number of groups in the kth compound, and K the total number ofcompounds considered for the least-squares fitting of GC values. The experimental enthalpies offormation were taken from the most recent compilation available in the literature. 8 wk was setinversely proportional to the squared uncertainty in the experimental AfH;9 8,k. With this choice,the experimental data with smaller uncertainty are given more weight during least-squaresminimization.

The best set of the GC values were derived as follows: GC[CB-(CB)3] = 0.331 kcal/mol,GC[CF-(CB) 2 (CF)I = 1.083 kcal/mol, GCICF-(CB)(CF)21 = 1.162 kcal/mol and GC[CF(CF) 31 =2.879 kcal/mol. The AM1-GC enthalpies of formation are close to experimental values, with anaverage deviation of 1.4 kcal/mol per molecule for unsubstituted benzenoid aromatic compounds.Calculations for large peri-condensed aromatic compounds to 3-circumcoronene (C150 H9 6 )indicated that the enthalpies of formation predicted by the AM I-GC method extend smoothly to thatof the limit of a graphite monolayer.

The GC values were also derived for the substituents and radical groups including CB-CH3,>CB-.C2H5 , >CB-C 2H 3, >CB-C 2H, cyclopentenyl ring group, >CB-CB<, >CB* and >CB-CH=CH. The enthalpies of formation for several families of structural isomers, namely a series ofclosely related methyl- and ethyl-substituted aromatics were examined. The results indicate that thepresent GC-AM1 method is capable of accurately predicting not only the absolute values of Af/ 9 8(to a few tenths of kcal/mol), but also the relative stability of these structural isomers. The sameaccuracy was not obtained when the similar MNDO-GC method was used.

We also examined the stability of aryl radicals as functions of molecular size and radicalposition. The bond dissociation energies were obtained from the AMI-GC enthalpies offormation. Examination of these BDE values indicates that the strength of aryl-H bond isessentially independent of molecular size, but dependent on the neighboring geometry of the C-Hbonds. The calculated BDE values can be placed into three groups according to type of the aryl-Hbonds, i.e., group a, b and c depicted in the following diagram:

HH ýbk a a H

H -

H N cC 2H

Hb aHH

The aryl-H bonds of group b are weaker than those of group a by 1-2 kcallmol. Theoptimized AMLI geometries of the molecules having aryl-H bonds of group b appear to have eithera twisted plane or deformed six-member rings, which is apparently a result of steric repulsionbetween the two H atoms on the edge of the bay area. Lower strength of aryi-H bonds of group bis thus the result of this larger steric repulsion. The steric repulsion is further increased by about 3kcallmol in group c.

9

A summary of the calculated enthalpies of formation of PAH molecules and radicals pertinentto PAH formation in flames are summarized in the following table.

molecules Af-2J98 (kcal/mol) radicals AfH298 (kcal/mol) BDE

AMI AM1-GC AMI AM1-GC (kcal/mol)

benzene 22.0 20.0 phenyl 79.5 78.6 110.7naphthalene 40.6 35.8 1-naphthyl 98.4 94.7 111.0

2-naphthyl 98.0 94.3 110.6biphenyl 47.6 43.4 2-biphenyl radical 105.1 W02.0 110.7

3-biphenyl radical 105.3 102.2 110.94-biphenyl radical 105.2 102.1 110.8

phenanthrene 57.4 49.6 l-pherianthryl 115.2 108.5 111.02-phenanthryl 115.2 108.5 111.03-phenanthryl 114.8 108.1 110.64-phenanthryl 114.2 107.5 110.09-phenanthryl 114.9 108.2 110.7

anthracene 62.9 55.3 1-anthryl 120.4 113.9 110.72-anthryl 120.2 113.7 110.59-anthryl 121.2 114.7 111.5

pyrene 67.3 53.9 1-pyrenyl 125.3 113.0 111.22-pyrenyl 124.7 112.4 110.64-pyrenyl 124.7 112.4 110.6

benzotelpyrene 84.0 67.5 binzo[elpyren-1-yl 140.3 124.8 109.4benzo[elpyren-5-yl 140.2 124.7 109.3

benzo(ghulperylene 91.3 69.2 benznfghilperylen-1-yl 148.0 126.9 109.8coronene 96.2 68.5 coronyl 153.9 127.2 110.8

acenaphthylene 80.7 62.1 3-acenaphthyl 139.2 121.3 111.74-acenaphthyl 139.2 119.7 111.75-acenaphthyl 138.7 121.9 111,4

acephenandtrylene 95.9 74.3acepyrenylene 109.5 82.3

ethynylbenzene 76.5 73.8 2-ethynylphenyl 134.8 133.2 111.53-ethynylphenyl 134.3 132.7 111.04-ethynylphenyl 134.0 132.4 110.7

1,2-diethynylbenzene 132.4 129.01-ethynylnaphthalene 96.1 90.6 8-ethynylnaphth-1-yl 154.1 149.3 110.84-ethynylphenanthrene 117.6 109.1 5-cthynylphenanthr-4-yl 171.3 163.9 106.94-ethynylpyrene 123.1 109.0 4-ethynylpyren-5-yl 180.9 167.9 111.04-ethynylacenaphthylene 135.4 116.15-ethynylacenaphthylene 135.7 116.4

styrene (ethenylbenzene) 38.7 35.4 styryl 88.5 94.6

10

Transport Properties of Polycyclic Aromatic Hydrocarbons

The transport properties of aromatic compounds, especially the gaseous binary diffusioncoefficients, are key components in modeling PAH formation in hydrocarbon flames. As part ofthe ongoing -. oject, the Lennard-Jones self-collision diameters and well depths of 29 polycyclicaromatic hydrocarbons were derived using a group contribution technique for the estimation ofcritical temperatures and pressures and the Tee-Gotoh-Stewart correlations of corresponding states.

The estimation of gaseous binary diffusion coefficients of PAH compounds involves thedetermination of LU self-collision diameters o* and well depths e. Values of a and e are oftenderived from viscosity measurements. However, only a limited number of such measurements areavailable for PAHs. A review of the available physical property data of aromatic compoundsindicated that at present the most complete set of data is for the normal boiling point. Based on thisconsideration, we employed a group contribution technique which correlates the criticaltemperature of a substance with its normal boiling point and critical pressure with molecularweight. The critical temperature and pressure obtained in this manner were then used to estimatethe U self-collision diameter and well depth using the correlations of corresponding statesdeveloped by Tee, Gotoh and Stewart: 9

l'013Pc )1/3 = 2.3551 - 0.0874o) (3)

and

-= 0.7915 + 0.1693w (4)kBTc

where P, and T, are critical pressure and temperature in bar and K, respectively, and k8 theBoltzmann constant. The acentric factor, co. is a macroscopic measure of the extent to which theforce field around a molecule deviates from spherical geometry. The empirical constants in Eqs.(3) and (4) were obtained from the viscosity and second virial coefficient data of 14 substancesranging from inert gases to benzene and normal heptane. The correlations were shown to provideaccurate estimations of viscosity with an average deviation of 2.57 %. In this study, we appliedEqs. (3) and (4) to PAH compounds.

The critical temperature Tc and pressure Pc were estimated following a group contributiontechnique. This technique was recently re-examined and updated by Somayajulu, 10 whosuggested the following relations:

Tb l1.242 + 0.138Nt (5)S-Tb

and

PC03 Mw jf2 = 0.339 + 0.226Np, (6)

11

where Tb is the boiling temperature in K, Mw the molecular weight in kg/mol, and N, and Np arethe temperature and pressure indices of a molecule, respectively, and are calculated as the sums ofthe molecular structural group indices, i.e., Nt = En, and Np = Y-np. The values of nt and npwere obtained by Somayajulu10 through evaluation of the experimental T' and P, data ofhydrocarbons from small alkanes to aromatics of the size of anthracene and phenanthrene. Theacentric factor co in Eqs. (3) and (4) was evaluated using the Lee-Kesler vapor-pressure relations1 1which give

0) = -ln(1.013Pc)-5.927 + 6.0960-1 + 1.2891n 0-0.16996 (7)15.252-15.6880- - 13.4721n 0+0.4360 6

where 9 = TWTC.The normal boiling points (at 1 atm) of 29 selected PAH compounds were taken from the

most recent compilation of CRC Handbook. 12 The U_ parameters were then evaluated using Eqs.(3)-(7). The obtaited cr.and E values are plotted against molecular weight in Fig. 2. Also includedin this figure are the data for molecular hydrogen and selected small hydrocarbon compoundsreported by Svehla. 13 As can be seen, the LJ parameters of PAHs correlate strongly withmolecular weight. These correlations can be expressed by

1 = t.234 (103Mw)0° 33 (A) (8)and

E/kB = 37.15 (103Mw)°058 (K), (9)where Mw is in kg/mol.

Given the LJ collision diameters and well depths, the gaseous binary diffusion coefficientswere evaluated with the Chapman-Enskog equation

3 "•i2ff(kBT)3 /pdiDij = V' o.(.T fD, (10)

where P is the pressure, T the temperature, S2 the collisional integral, M qij the reduced mass ofspecies i and j, fD is a correction term (1.0 < fD < 1.1) and was assumed here to be equal to unity.Eq. (10) is valid at low pressures when the ideal gas law is applicable. The calculation of Dij wasfacilitated by a computer code developed by Kee et al. 14 In addition, a second approach based onthe Fuller approximation 15 was taken for the analysis of the diffusion coefficients,

0.3162T I75 i + ]1 MwiMw.j

1. 01 3P [(Yu)" + (Y_)1/32

where T is in K, P in bar, Mw'i and Mw,j the molecular weights of binary components i and j inkg/mol, respectively, and v the atomic diffusion volume.

In Fig. 3, the binary diffusion coefficients calculated using the estimated LU parameters arecompared with those obtained with the Fuller approximation 15 for naphthalene-, pyrene-, and

12

ovalene-N 2 binary mixtures at a pressure of I atm. The U parameters o1 ovalene were obtainedwith Eqs. (8) and (9). As seen in Fig. 3, the agreement between the two methods for the estimatedbinary diffusion coefficients of naphthalene in N2 is very good. For pyrene and ovalene, theFuller approximation 15 gave estimates that are about 10 and 15 % higher, respectively, than thosederived with the estimated U parameters. Considering the fact that both approaches have not beentested for molecules of sizes as large as ovalene, the agreement should be considered as good. Thegood agreement between the results obtained with Eq. (11) and with the derived U parametersprovide a cross check for the developed U-parameter method. The LJ parameters derived in thisstudy can be added to the existing transport database, such as that available with the Sandia burnercodes.

9 1200

8 10000

0

7 800

2 0-. =600 0

4 400

4 A

3 / 200 A

2 0 ' ,0 50 100150200250300350 0 50 100150200250300350

MW (g/mol) Mw (g/mol)

Figure 2. Lennard-Jones collision diameter (left) and well depth (right) plotted as a function ofmolecular weight. Circles and diamonds: PAH molecules of this study, triangles: smalllinear hydrocarbon molecules and H2, solid lines: Eqs (8) and (9), fitted to the datagiven by the circles.

13

2.5

from U parameters, eq. (10)

Fuller approximation, eq. (I)

2.0

x 1.0

05 naphthalene >

rovalene0.0

0 500 1000 1500 2000

T (K)

Figure 3. Comparison of gaseous binary diffusion coefficients obtained from the LJ collision

diameters and well depths and from the Fuller approximation15 for naphthalene-,

pyrene-, and ovalene-N2 mixtures at a pressure of I atm.

14

, - .•m •• m m 1.0I I III I I II II

naphthalen

Semiempirical Quantum-Mechanical and RRKM Studies of Reaction C8 H7÷ + C2H2 --* CIoH9

We have completed our theoretical study on the title ion-molecule reaction. This reaction isone of the key steps in the mechanism proposed by Calcote and coworkers. 16 Seven majorisomers for the C10 H9 + adduct and II possible product channels were identified in our study,indicating the complexity of the reaction. The energetics and molecular parameters of the reactants,intermediate species, products, and transition states were evaluated using the semiempiricalquantum-mechanical AMI method. The rate coefficients and their pressure and temperaturedependence were then calculated based on the RRKM theory with a full consideration of angularmomentum conservation. The microscopic rate coefficients for the reaction channels involving thedissociation of the energized complexes were determined with the microcanonical variationaltransition state theory. RRKM calculations were performed for temperatures from 300 to 2000 Kand at a pressure of 20 torr. These conditions are the same as our previous kinetic modeling studyof ion formation in flames. The major results of this study can be summarized as follows: (1) attemperatures lower than 1000 K, the major reaction channels are to form the two most stableCIoH9 + isomers

H

+ C2HN (12a)

(12b)

The overall rate coefficient of the above two reactions at T < 1000 K is equal to that of theLangevin limit, 6x10 14 cm 3mol-is-l; (2) at flame temperatures (1500K <T< 2000K), the overallrate coefficients are more than an order of magnitude lower than the Langevin limit. The majorproducts are those from the addition/dissociation channels, i.e.,

H

S(12c)

+ +H 2 (I 2d)

The computed rate coefficients of (1 2c) and (1 2d) in the 1500 to 2000 K temperature window areabout lxl0 13 and 3x10 1 3 cm 3mol-[s-I, respectively. The latter result suggests that the ratecoefficients used in the reaction model of ion formation proposed by Calcote and coworkers 16 maybe an order of magnitude too high.

15

FUTURE WORK

The objectives for the next year are the following:

1. To complete the revision and testing of the neutral reaction mechanism of PAH formation andgrowth, and to prepare a manuscript summarizing the results.

2. To continue a computational study of pressure effect on soot formation.

3. To perform computer simulation of soot formation in benzene flames. This is a part of theoverall proposed work, in the context of developing and testing models of soot formation inmore complex environments. The ability to predict soot formation in flames of aromatics,consistently with the predictions for soot formation from non-aromatic hydrocarbons, is thenext important milestone towards simulation of soot formation from fuel blends of practicalimportance.

4. To investigate the details of the surface growth kinetics of soot particles. This is one of the keyfactors affecting the accuracy of soot model predictions in realistic combustion environments.A detailed study of the processes involved will be studied using our newly developedtheoretical techniques for gas-surface reaction kinetics.

5. To prepare a manuscript reporting the results obtained in the theoretical study on a bench-markion-molecule reaction, C8H7' + C2H2 -- C10H9+.

6. To initiate computer simulation of soot formation in more practical environments, like diffusionflames and/or diesel engines.

PRESENTATIONS AND PUBLICATIONS

I. M. Frenklach, "Chemistry of Particle Forming Systems," Engineering Foundation Conferenceon Vapor Phase Manufacture of Ceramics," Kona, Hawaii, January 12-17, 1992 (Invited).

2. M. Frenklach, "Development of Predictive Reaction Models of Soot Formation," AFOSRContractors Meeting on Propulsion, La Jolla, CA, June 15-19, 1992.

3. M. Frenklach, "Mechanism of Soot Particle Formation," Scientific Conference on Obscurationand Aerosol Research, Aberdeen Proving Ground, MD, June 22-25, 1992 (Invited).

4. M. Frenklach, "The Chemistry and Modeling of Soot Formation," Caterpillar Inc., EngineDivision Engineering, July 8, 1992.

5. H. Wang and M. Frenklach, "Enthalpies of Formation of PAH Molecules and Radicals," Tobe presented at the Joint Technical Meeting oi the Central and Eastern States Sections of theCombustion Institute on Combustion Fundamentals and Applications, New Orleans, March15-17, 1993.

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6. M. Frenklach and H. Wang, "Detailed Mechanism and Modeling of Soot ParticleFormation," in Mechanisms and Models of Soot Formation (H. Bockhorn, Ed.), Springer-Verlag, Heidelberg, in press.

7. M. Frenklach and H. Wang, "Detailed Mechanism and Modeling of Soot Formation," inAdvanced Combustion Science (T. Someya, Ed.), Springer-Verlag. in press.

8. H. Wang and M. Frenklach, "Enthalpies of Formation of Benzenoid Aromatic Molecules andRadicals," J. Phys. Chem., in press.

9. P. Markatou, H. Wang and M. Frenklach, "A Computational Study of Sooting Limits inLaminar Premixed Flames of Ethane, Ethylene and Acetylene," Combust. Flame, submitted.

10. H. Wang and M. Frenklach, "Lennard-Jones Parameters and Gaseous Diffusion Coefficientsof PAHs in He, Ar, H2 , N2 and Air at Low Pressures," J. Phys. Chem. Ref. Data,submitted.

PROFESSIONAL PERSONNEL

Dr. Michael Frenklach - Principal Investigator

Dr. Brian Weiner - Participating FacultyDr. Penelope Markatou - Postdoctoral Scholar

Mr. Hai Wang - Graduate Student

Mr. Sergei Kazakov - Graduate Student

INVENTIONS

None.

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REFERENCES

1. Harris, M. M., King, G. B., and Laurendeau, N. M., Combust. Flame 64, 99 (1986); 67,269 (1987).

2. Kee, R. J., Grcar, J. F., Smooke, M. D., and Miller, J. A., Sandia Report No. SAND85-8240, Sandia National Laboratories, Livermore, California, 1985.

3. Frenklach, M., and Wang, H., "Detailed Mechanism and Modeling of Soot ParticleFormation," in Mechanisms and Models of Soot Formation (H. Bockhorn, Ed.), Springer-Verlag, Heidelberg, in press.

4. Frenklach, M., and Wang. H., Twenty-Third Symposium (International) on Combustion,The Combustion Institute, Pittsburgh, 1991, p. 1559.

5. Wild, G., Science 101, 653 (1945).

6. Stein, S. E., and Fahr, A., J. Phys. Chem. 89, 3714 (1985).

7. Disch, R. L., Schulman, J. M., and Peck, R. C., J. Phys. Chem. 96, 3998 (1992).

8. Pedley, J. B., Naylor, R. D., and Kirby, S. P., Thermochemical Data of OrganicCompounds; Chapman and Hall, London, 1986.

9. Tee, L. S., Gotoh, S., and Stewart, W. E., I&EC Fundamentals 5, 356 (1966).

10. Somayajulu, G. R. J., Chem. Eng. Data 34, 106 (1989).

11. Lee, B. 1., and Kesler, M. G., AIChE J. 21, 510 (1975).

12. Handbook of Chemistry and Physics, 71 th edition, edited by D. R. Lide (CRC Press, BocaRaton, Florida, 1990/1991).

13. Svehla, R. A., NASA Technical Report R-132. Lewis Research Center, Cleveland, Ohio,1962.

14. Kee, R., Warnatz, J., and Miller, J. A., Sandia Report No. SAND83-8209, Sandia NationalLaboratories, Albuquerque, New Mexico, 1983.

15. Fuller, E. N., Ensley, K., and Giddings. J. C., J. Phys. Chem. 73, 3679 (1969).

16. Calcote, H. F. and Gill, R. J., "Computer modeling of soot formation comparing free radicaland ionic mechanisms," Final Report to AFOSR. TP-495, 1991.

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